Question: Solve for $x$ and $y$ using substitution. ${-3x+y = 7}$ ${y = -4x-7}$
Solution: Since $y$ has already been solved for, substitute $-4x-7$ for $y$ in the first equation. ${-3x + }{(-4x-7)}{= 7}$ Simplify and solve for $x$ $-3x-4x - 7 = 7$ $-7x-7 = 7$ $-7x-7{+7} = 7{+7}$ $-7x = 14$ $\dfrac{-7x}{{-7}} = \dfrac{14}{{-7}}$ ${x = -2}$ Now that you know ${x = -2}$ , plug it back into $\thinspace {y = -4x-7}\thinspace$ to find $y$ ${y = -4}{(-2)}{ - 7}$ $y = 8 - 7$ $y = 1$ You can also plug ${x = -2}$ into $\thinspace {-3x+y = 7}\thinspace$ and get the same answer for $y$ : ${-3}{(-2)}{ + y = 7}$ ${y = 1}$